Polynomial alias higher degree fuzzy transform of complex-valued functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27510%2F18%3A10236821" target="_blank" >RIV/61989100:27510/18:10236821 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61988987:17610/18:A1901GGE

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.fss.2017.06.011" target="_blank" >http://dx.doi.org/10.1016/j.fss.2017.06.011</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2017.06.011" target="_blank" >10.1016/j.fss.2017.06.011</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Polynomial alias higher degree fuzzy transform of complex-valued functions

Popis výsledku v původním jazyce

In this article, we propose a general approach to the computation of components of the direct higher degree fuzzy transform. Apart from the orthogonal bases of the subspaces of polynomials of weighted Hilbert spaces with respect to a generalized uniform fuzzy partition, which are used in all papers on fuzzy transform of higher degree, we admit also the non-orthogonal bases. An advantage of using non-orthogonal bases consists in the possibility of replacing orthogonal polynomials, derivation of which by the Gram-Schmidt orthogonalization process can be questionable difficult or imprecise, by suitable non-orthogonal polynomials of much simpler form. We present a simple matrix calculus and show how it can be used to introduce the components of the direct higher degree fuzzy transform. With the help of the monomial basis, we prove a convergence theorem and an approximation theorem for the higher degree fuzzy transform. The results are illustrated by examples including a comparison with standard methods.

Název v anglickém jazyce

Polynomial alias higher degree fuzzy transform of complex-valued functions

Popis výsledku anglicky

In this article, we propose a general approach to the computation of components of the direct higher degree fuzzy transform. Apart from the orthogonal bases of the subspaces of polynomials of weighted Hilbert spaces with respect to a generalized uniform fuzzy partition, which are used in all papers on fuzzy transform of higher degree, we admit also the non-orthogonal bases. An advantage of using non-orthogonal bases consists in the possibility of replacing orthogonal polynomials, derivation of which by the Gram-Schmidt orthogonalization process can be questionable difficult or imprecise, by suitable non-orthogonal polynomials of much simpler form. We present a simple matrix calculus and show how it can be used to introduce the components of the direct higher degree fuzzy transform. With the help of the monomial basis, we prove a convergence theorem and an approximation theorem for the higher degree fuzzy transform. The results are illustrated by examples including a comparison with standard methods.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

50206 - Finance

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fuzzy sets and systems

ISSN

0165-0114

e-ISSN

—

Svazek periodika

342

Číslo periodika v rámci svazku

July

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

31

Strana od-do

1-31

Kód UT WoS článku

000432350400001

EID výsledku v databázi Scopus

2-s2.0-85023622557